Fine derby strikes from Peter Crouch, Steven Gerrard and Djibril Cisse embarrassed the hosts' defence, though James Beattie did at least end Liverpool's record run of clean sheets. Everton worked hard, feeding on the passion flowing from the terraces, but some of their competitive edge slipped over into excess.
Phil Neville and Mikel Arteta walked for double yellows and received further censure when their manager, David Moyes, arrived in the dressing room. "The two boys were stupid," he said. "They were on bookings. They wanted to show they care, that it mattered. I would rather have them that way, than the other. But they know they let their team-mates down." Everton will also be fined £25,000 for having six players booked.
Moyes stressed that his commitment to the job remained undimmed. "I'll be there on the touchline next week," he said. "I'll stand up to be counted. We have to keep believing."
Belief is etched on Liverpool's movements. Last night was all about confidence, pace and power against uncertainty, European champions against a side on the slide: Liverpool were a class - let alone a local park - apart from their neighbours last night.
"We've now got the bragging rights until the next derby," said Gerrard, before re-focusing his thoughts upwards on the title race. "Chelsea are a fantastic side. We've just got to concentrate on our own game and carry on winning."
Everton's programme presciently described the visitors as a "mean machine" and Liverpool have certainly acquired the ruthlessness to roll over lesser opposition. At one point early in the second half, Gerrard sped past Simon Davies and Neville, who crashed into each other like rookie policemen chasing a street-wise pickpocket.
Inspired by their captain, playing with terrific speed of thought and movement, Liverpool were Everton's superiors, master craftsmen giving a lesson in the footballing arts and sciences to callow apprentices.
Within 11 minutes, Liverpool were ahead, the ball speeding from Momo Sissoko to Cisse and then Gerrard, whose clever header down the inside-right channel deceived Everton's defence and allowed Crouch a clear run at Nigel Martyn. Crouch calmly rounded Martyn and drove in his sixth goal of the month.
One became two after 17 minutes. When Martyn punched a Gerrard free kick out, Xabi Alonso and Sami Hyypia worked the ball right to Steve Finnan. The full-back's cross was headed out by Tim Cahill but only to Gerrard. The ball was swiftly dispatched past Martyn, with a slight deflection off Joseph Yobo. Goodison was aghast.
Perhaps anticipating their manager's half-time wrath, Moyes' players stirred themselves to score a fine goal, so wrecking Liverpool's hopes of breaking the club record of nine clean sheets set in 1923. Here, finally, were Everton attacking with precision and belief, moving the ball swiftly to catch out their visitors' noted back-line.
Arteta did well down the right, scooping the ball across to the far post, where Kevin Kilbane headed back. Davies took the ball on his chest and flicked it on towards Beattie. The Everton striker had hitherto looked alarmingly static against Jamie Carragher and Hyypia, but he did well here, leaping up, twisting his body to glance a header into the net.
"We were disappointed to concede just before half-time, and we were expecting a battle in the second half," Carragher said.
Not for long. Shortly after the re-start, Weir played Cisse onside and Everton were left exposed. Cisse galloped on, avoided Weir's despairing challenge before curling the ball brilliantly past Martyn. "That goal killed the game off," added Carragher.
Worse befell Everton. They were denied a legitimate-looking goal when Beattie headed home, only for Cahill's cross to be deemed out. Then Neville departed for fouls on Cisse and Sissoko. Beattie then missed a sitter before Arteta followed Neville down the tunnel for fouls on Hyypia and Luis Garcia.
Everton now travel to Sunderland on Saturday for a match that will be high on anxiety but low on beauty. Liverpool's 'mean machine' rolls on.